Problem 413

{{searchResults.length}} results for “{{searchWords}}” No results found for “{{searchWords}}” × back to contents

§{{x[0]}} {{x[1]}}

Table of Contents

Problem 413: (2025 AMC 12a, 11)

The orthocenter of a triangle is the concurrent intersection of the three (possibly extended) altitudes. What is the sum of the coordinates of the orthocenter of the triangle whose vertices are $A(2,31), B(8,27),$ and $C(18,27)$? $\textbf{(A)}~5\qquad$ $\textbf{(B)}~17\qquad$ $\textbf{(C)}~10+4\sqrt{17} +2\sqrt{13}\qquad$ $\textbf{(D)}~\frac{113}{3}\qquad$ $\textbf{(E)}~54$

Solution

Exercise 413: Solution

The orthocenter of a triangle is the concurrent intersection of the three (possibly extended) altitudes. What is the distance from the origin to the orthocenter of the triangle whose vertices are $A(-3,10)$, $B(1,2)$, and $C(9,2)$?

Search Go to Prev Next

Contact Us